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The Systems of
Order in Music


in Understanding as Reflected by Language

The Beginnings of
Musical History

New Sound Composer
of the 20th Century and the
Range of Intervals

to the Transcendental
Play of Music

Musical Insight into the Culture of Peoples

Musical Relationships

The Musical Path
to Self-Knowlegde



The Counterpoint

The Threefold Perfect
Form of the Harmony

Relations in Music


Peter Hübner
Founder of the
Micro Music Laboratories




  The Systems of Order in Music
Advancing to the Transcendental Play of Music

Nev­er­the­less, there is a way to go be­yond that bor­der to dis­har­mony. The ob­sta­cle, namely the lack of con­trol over the in­stru­ment, which the clas­si­cal com­pos­ers were faced with, can be over­come as soon as we rec­og­nize the in­ner world of the mu­si­cal sound-space – that is, to fathom our in­ner think­ing by means of our in­ner hear­ing, and to rec­re­ate the tran­scen­den­tal play of mu­sic from there.

The Obstacle in the Mastery over the Instrument
Due to a great amount of sci­en­tific re­search and a re­cent im­prove­ment of our habits of hear­ing we know to­day that a tone is not just a tone. We know that, in the so-called tone, lies a hid­den world which had been ignored so far by con­ven­tional mu­sic and even by mu­sic the­ory. Fur­ther­more we know that, pro­ceed­ing from the mu­sic of the clas­si­cal and ro­man­tic pe­ri­ods, true pro­gress, so nec­es­sary to­day, is only pos­si­ble through the mas­tery over the mi­cro­cosm of mu­sic. This redis­cov­ery of the mi­cro­cosm of mu­sic is closely linked to the re­vival of mu­sic as such.

Tone Analysis
The fact that the third for ex­ample is to­day con­sid­ered “corny,” and in­deed stimu­lates sen­ti­men­talism in the masses, calls for fur­ther re­fine­ments which were so far im­pos­si­ble due to the de­fi­cient con­ven­tional train­ing of mu­si­cians. Such an ad­vance­ment through the mas­tery over the mu­si­cal mi­cro­cosm is fully in line with the con­cepts of the great clas­si­cal com­pos­ers and blends smoothly with their own mu­si­cal ac­com­plish­ments.

The Refinement of Tonality
In the his­tori­cal de­vel­op­ment of the tech­nique of com­po­si­tion the oc­tave-par­al­lels were em­ployed first. At the time of the fifth, the smaller in­ter­val, the oc­tave par­al­lels were con­demned due to their “gross­ness.” The dis­pute among the ex­perts, con­cern­ing the oc­tave par­al­lels and the fifth par­al­lels, lasted for quite some time and was fi­nally set­tled in fa­vour of the fifth par­al­lels, which are finer dif­fer­en­ti­ated.

Refinement of Comprehension
The fourth is that in­ter­val which com­ple­ments the fifth to be­come an oc­tave, and it can thus be re­garded as the re­verse of the fifth with re­spect to the oc­tave. There­fore, the fourth in its prac­ti­cal use may, and his­tori­cally has been, roughly equated with the fifth.

The Fourth as the Reverse of the Fifth
Dur­ing the era of the fifth and the fourth, the oc­tave and the third came un­der at­tack – the for­mer be­ing the past and the lat­ter the fu­ture in­ter­val. How­ever, once the mod­ern ad­vo­cates of com­po­si­tion had won the his­tori­cal victory in fa­vour of the third – cre­at­ing an in­flu­ence that reaches even into our time – the oc­tave and the fifth par­al­lels, then re­garded as gross, were banned from the com­po­si­tion les­sons at schools and acad­emies. To this day, we still find this pro­hi­bi­tion, even though any con­ven­tion­ally played in­stru­ment, sim­ply by its very na­ture, con­stantly pro­duces oc­tave and fifth par­al­lels, a fact that can be eas­ily proven with an oscilloscope.

Prohibiting the Conventional in the Study of Music
There­fore, in to­day’s con­ven­tional com­po­si­tion les­sons mainly the third in­ter­val, and by the “most mod­ern” the sec­ond, is glo­ri­fied – and be­ing par­al­lels, they both will, in the fore­see­able fu­ture, most likely be ban­ished from com­po­si­tion les­sons, in much the same way we have wit­nessed in the past in the case of the oc­tave and the fifth par­al­lels.

The Conventional Compositional Instruction
The men­tal nar­row­ness of such an ex­tro­vert, unmu­si­cal con­sid­era­tion of the com­po­si­tional ele­ments seems al­most gro­tesque to an ob­server who knows the ac­tual spec­trum of over­tones – and be it only from the stand­point of physi­cal meas­ure­ments – and forces us all to read­just our think­ing if we are con­cerned with true mu­sic.

The Mental Narrowness of the Conventional Viewpoint on Compositional Elements
A dog is no more im­por­tant in crea­tion than a cat, and some­times the one or the other ani­mal ap­pears more prominently in the lively di­ver­sity of our world – at times they even may appear to­gether har­mo­ni­ously. Like­wise, the ele­ments of the mu­si­cal sound-space, the over­tones with their re­la­tions, the in­ter­vals, appear in the world of mu­sic in many dif­fer­ent ways, dis­play­ing vary­ing de­grees of re­la­tion­ship.

Natural Relations in the Overtone-Spectrum
In the natu­ral spec­trum of over­tones all neighbours main­tain good re­la­tions. The pres­ence of stronger and weaker sounds in the natu­ral or­der of the over­tones is an in­di­ca­tion of a very natu­ral hi­er­ar­chy in which the stronger sound re­quires more space for it­self than the weaker sound.
When an in­stru­ment is be­ing played, the ba­sic tone there­fore is usu­ally very loud, and the over­tones, that are built succcessively upon the ba­sic tone, sound less and less while the space be­tween the in­di­vid­ual over­tones si­mul­ta­ne­ously be­comes in­creas­ingly nar­row.

The Hierarchy of Sounds in the Spatial Expansion
Ex­peri­ence in mu­sic teaches us that sub­tler over­tones, lo­cated at a greater dis­tance from the ba­sic tone, are more di­rectly ap­peal­ing to our more subtle in­ner-hu­man as­pects than the grosser over­tones which are closer to the ba­sic tone. There­fore, the un­fold­ment of the more and more subtle spec­tra of over­tones not only pro­vides a greater com­plex­ity in the mu­si­cal or­der of the sound-space, but also lays the foun­da­tion for a com­pletely new sys­tem of in­fi­nite mu­si­cal di­ver­sity.

Inner View of the Tonality
Only through the natu­ral, ar­tis­tic mas­tery over the subtle spec­trum of over­tones of a sound the very life of mu­sic is made ac­ces­si­ble – that se­cret power, that se­cret magic which con­sti­tutes true mu­sic.

Penetrating the Life of Music
To make the mi­cro­cosm of mu­sic au­di­ble – those subtle and ever more subtle spec­tra of over­tones and their ever more closely spaced tones – is the re­ward­ing timely task for the in­stru­men­talist of to­day.

Making the Microcosm of Music audible
To­nal­ity is the world of the so­cio­logi­cal stan­dards of mu­sic, and the melody, which moves in a to­nal­ity cre­ated of the natu­ral spec­trum of over­tones, re­mains, de­spite its di­ver­sity, within the stan­dards of that so­cial or­der of over­tones – the to­nal­ity.

Tonality as the World of Sociological Musical Standards
In com­plete ap­pre­cia­tion of natu­ral, tonal re­la­tions the motif moves as the melody within the to­nal­ity, and within these great so­cial laws it es­tab­lishes, de­ter­mined by the har­mony, its natu­ral re­la­tion­ship with the other mo­tifs that take part in the mu­si­cal event.

Tonal Relations
Within a sound­ing so­cial frame­work which is ruled by the to­nal­ity, po­lyph­ony de­scribes, in terms of this un­der­stand­ing, the de­vel­op­ment of the vari­ous mo­tifs in the form of vari­ous melo­dies. More­over, in an in­te­grated world of many such so­cial struc­tures, po­lyph­ony forms the me­lo­di­ous de­scrip­tions of the de­vel­op­ment of many mo­tifs sharing a com­mon goal un­der very dif­fer­ent so­cial cir­cum­stances.

Polyphony and the Social Structures of Music
Natu­rally, this un­der­stand­ing of com­pos­ing re­quires a syn­the­sis of com­po­si­tion and in­stru­men­ta­tion – two spe­cial­ized fields which even to­day are still taught sepa­rately and there­fore behave al­most like steppar­ents to­wards mu­sic.

A New Understanding of Composition
  With kind permission of AAR EDITION INTERNATIONAL